6. Inhibition

6.1. Reversible and Irreversible Inhibitions

Sometimes the effect of an inhibitor can be reversed by decreasing the concentration of inhibitor (e.g. by dilution or dialysis). The inhibition is then said to be reversible. If, once inhibition has occurred, there is no reversal of inhibition on decreasing the inhibitor concentration the inhibition is said to be irreversible; irreversible inhibition is an example of enzyme inactivation. The distinction between reversible and irreversible inhibition is not absolute and may be difficult to make if the inhibitor binds very tightly to the enzyme and is released very slowly. Reversible inhibitors that behave in a way that is difficult to distinguish from irreversible inhibition are called tight-binding inhibitors.

6.2. Linear and Non-Linear Inhibition

Sometimes the effect of an inhibitor I can be expressed by multiplying one or more of the terms in the denominator of the general rate expression (Eqn 13) by factors of the form (1 + [I]/K_i). The inhibition is then said to be linear and K_i which has the dimensions of a concentration, is called an inhibition constant for the inhibitor I. The word linear in this definition refers to the fact that the inhibition is fully specified by terms in the denominator of the rate expression that are linear in inhibitor concentration, not to the straightness of any plots that may be used to characterize the inhibition experimentally.

If the inhibition cannot be fully expressed by means of linear factors in the denominator the inhibition is said to be non-linear.

Linear inhibition is sometimes called complete inhibition, and the contrasting term partial inhibition is sometimes used for a type of non-linear inhibition in which saturation with inhibitor does not decrease the rate to zero. These latter terms are discouraged because they can be misleading, implying, for example, that the rate may indeed be decreased to zero in 'complete inhibition' at non-saturating concentrations of inhibitor.

6.3. Degree of Inhibition

If a reaction occurs in the absence of inhibitor with rate v₀ and in the presence of inhibitor with rate v_i, the degree of inhibition is defined as

. . . . . . . . (20)

As this quantity is a ratio of rates it is dimensionless. The subscripts '0' and 'i' are useful for distinguishing between uninhibited and inhibited reactions respectively when they are required together, but are usually omitted when no confusion is likely.

6.4. Classification of Inhibition Types

Provided that an enzyme behaves in accordance with the limiting behaviour described in Section 4.1 both in the absence of inhibitor (which is always true if Michaelis-Menten kinetics are obeyed and is also true more generally), the type of inhibition may be classified according to whether it affects the apparent value of k_A, the apparent value of k₀, or both.

If the apparent value of k_A is decreased by the inhibitor the inhibition is said to have a competitive component, and if the inhibitor has no effect on the apparent value of k₀ the inhibition is said to be competitive.. In linear inhibition there is a linear effect on 1/ :

. . . . . . . . (21)

and the constant K_ic is called the competitive inhibition constant for I.

Conversely, if there is an effect on the apparent value of k₀ the inhibition has an uncompetitive component, and if the innibitor has no effect on the apparent value of k_A the inhibition is said to be uncompetitive. In linear inhibition there is a linear effect on 1/ :

. . . . . . . . (22)

and constant K_iu is called uncompetitive inhibition constant for 1.

If both competitive and uncompetitive components are present in the inhibition it is said to be mixed. The term non-competitive inhibition is sometimes used instead of mixed inhibition, but this usage is discouraged, first because the same term is often used for the special case of mixed inhibition in which K_ic = K_iu, second because it suggests that mixed inhibition is the antithesis of competitive inhibition whereas this description actually applies more accurately to uncompetitive inhibition, and third because the shorter word mixed expresses clearly the fact that both competitive and uncompetitive components are present.

Mixed inhibition as defined here encompasses such a broad range of behaviour that it may sometimes be helpful to subdivide it further. The case in which K_ic < K_iu may then be called predominantly competitive inhibition, the case with K_ic = K_iu may be called pure non-competitive inhibition, and the case with K_ic > K_iu may be called predominantly uncompetitive inhibition. The classical term for pure non-competitive inhibition was simply non-competitive inhibition, but this term has become ambiguous because of its widespread use for all kinds of mixed inhibition and because of this ambiguity it is discouraged for all purposes.

Both K_ic and K_iu have the dimensions of concentrations and may therefore be expressed in mol dm^-3, mol L^-1 or M. In contexts where distinction between K_ic and K_iu is unnecessary or inappropriate the general symbol K_i may be used for either. In the past there has been no generally understood symbol for the uncompetitive inhibition constant, which has been variously represented as K_i, K'_i, K_ii, etc. A new and unambiguous symbol seems required, therefore, and K_iu is proposed. Although the competitive inhibition constant has much more uniformly been expressed as K_i, the occasional use of the same symbol for the uncompetitive inhibition constant, together with the view that a logical and symmetrical symbolism is desirable, has suggested that the symbol K_ic should be used for the competitive inhibition constant whenever any ambiguity might attend the use of the more general symbol K_i.

As K_ic and K_iu can in principle be determined by measuring the effects of inhibitor on the slopes and ordinate intercepts respectively of plots of 1/v against 1/[A] they, have sometimes been symbolized as K_is (for K_i slope) and K_ii (for K_i intercept) respectively. Slopes and intercepts are not consistent from one kind of plot to another, however; for example, the slope and intercept in a plot of [A]/v against [A] correspond, respectively, to the intercept and slope of a plot of 1/v against 1/[A]. Such symbols are therefore ambiguous and should not be used except in explicit reference to particular plots.

In reactions with more than one substrate the classification of inhibitors as competitive, uncompetitive or mixed is not absolute but depends on which substrate is variable (in the sense of Section 5.2). For example, a particular inhibitor may cause variation in without any variation in when A is the variable substrate, but cause variation in both and when B is the variable substrate: it is then said to be a competitive inhibitor with respect to A but a mixed inhibitor with respect to B. In such systems the inhibition constants K_ic and K_iu refer to the limiting behaviour for saturating concentrations of all substrates except for the variable substrate. Inhibition constants observed at non-saturating concentrations of the constant substrates are apparent values and may be symbolized as and .

For some mechanisms some inhibition constants may be true dissociation constants. Whether this is true or not it does not form part of the definitions of the inhibition types and inhibition constants given above, which are purely operational, in keeping with the policy set out in Section 1. When symbols are required for the dissociation constants of particular species they should be explicitly defined in a way that avoids confusion with the operationally defined inhibition constants. A system of the following kind may be appropriate, but if used it should be explicitly defined in context. For a binary complex, e.g. EI, the dissociation constant may be symbolized as K with the name of the complex as subscript, e.g. K_EI For higher complexes where the nature of the dissociation needs to be specified, a full stop (period) may be used to separate the parts of the complex that dissociate from one another; for example, K_EI.S may be used for the dissociation of EIS into EI + S, whereas K_ES.I may be used for the dissociation of the same complex into ES + I.